Dynamical Systems and Poisson Structures
No Thumbnail Available
Date
2009
Journal Title
Journal ISSN
Volume Title
Publisher
Amer inst Physics
Open Access Color
OpenAIRE Downloads
OpenAIRE Views
Abstract
We first consider the Hamiltonian formulation of n=3 systems, in general, and show that all dynamical systems in R-3 are locally bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical system. The construction of the Poisson structures is based on solving an associated first order linear partial differential equations. We find the Poisson structures of a dynamical system recently given by Bender et al. [J. Phys. A: Math. Theor. 40, F793 (2007)]. Secondly, we show that all dynamical systems in R-n are locally (n-1)-Hamiltonian. We give also an algorithm, similar to the case in R-3, to construct a rank two Poisson structure of dynamical systems in R-n. We give a classification of the dynamical systems with respect to the invariant functions of the vector field (X) over right arrow and show that all autonomous dynamical systems in R-n are super-integrable. (C) 2009 American Institute of Physics. [doi:10.1063/1.3257919]
Description
Zheltukhin, Kostyantyn/0000-0002-1098-7369; Gurses, Metin/0000-0002-3439-3952
Keywords
[No Keyword Available]
Turkish CoHE Thesis Center URL
Fields of Science
Citation
WoS Q
Q3
Scopus Q
Source
Volume
50
Issue
11